#161
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#162

toyotathon posted: i sanded and then smoothed it using acetone. however, 3D printing is like making things with sticky rope, and between the ropes, there are crevices. this is where the acetone was hanging out when it was put in a rit bath. the acetone boiled out and created these bubbles of plastic along the crevices. it wasn't intentional but maybe it could be used to artistic effect. it messed up the dimensions unfortunately, but at least the hobby's cheap.

that's cool

#163

jansenist_drugstore posted:

i've been reading about the replicability crisis in social sciences (only one problem of an obvious many). on the one hand, so-called experts are saying that this is not a problem of a blind faith in p-values, but other so-called experts are saying that p-values can no longer be reliably used in research. came across bayesian statistics, and am wondering if anyone has any thoughts/experience about this approach to research or its usefulness in general? is this just another attempt to rationalize poor methods?

during my final year of undergrad i took a biopsych module, and after attending lecture one to doublecheck there was no attendance register, i safely ignored the next 59. after a relaxing evening reading a few wikipedia articles on biological psychology i was pretty confident walking into my finals only imagine the momentary horror as i read on the front of the paper "failiure to reference real research will cap your maximum mark"; well, i thought, fortune favours the bold, so i just scattered a few (allen, allen & smith, 2002) and Johnson and Johnson (1987) through the paper; 64%; my greatest ever own

#164
can i get a maths person to confirm that as a triangle drawn on a sphere has 3 right angles, a triangle drawn on the 4 dimentional equivilent of a sphere (3-sphere?) would have 4 right angles?
#165
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#166
that makes sense thanks: 180*(1 + 4 (1/8) = 270deg, cute

so if the triangle covers 1/4 it will = 360?, its not really a triangle then because one of the angles is a straight line at this point? like one side goes over the pole and another round the equator, so its just a big pacman mouth shape at this point, only got two sides...; i think ive jumped too far ahead in geometry with this, turns out i dont even know whata triangle is yet
#167
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#168
so you just invert the little area triangle? because any triangle drawn on a sphere automatically draws a miror triangle which covers the rest of the sphere..., so whenever you draw a triangle on a sphere you automatically enclose the whole sphere in two triangels
#169
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#170
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#171
so then what happens when you draw a triangle on a 4d sphere?
#172
can you draw three triangles without any space remaining. or 3d triangles, whatever,
#173
because obviously on a sphere when you draw 1 triangle you draw 2, but if you draw a third, you still only have two...
#174
if you make the two triangles join a side in such a way they form a bigger triangle together you can have 3 w/o space remaining
#175

toyotathon posted:

ain't math a kick

well heroditus says that pythagoras had some sort of proof for etenal life and stayed in his underground house for three years to the point where everyone thought he was dead then emerging in the fourth, so yes, i guess it has some charms

#176

lenochodek posted:

if you make the two triangles join a side in such a way they form a bigger triangle together you can have 3 w/o space remaining

oh i see, just divide the one in half; too simple, thanks.

#177

tears posted:

so then what happens when you draw a triangle on a 4d sphere?

this is a more complicated question since a triangle is really a 2d shape and a "4d" sphere (in the sense you mean) has 3 spatial degrees of freedom. you could still consider 2d triangles, in which case theres some ambiguity about how they would be embedded, or you could consider some related polyhedron, like a tetrahedron. im not sure about the exact answer to your question in those cases though, sorry....

#178
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#179
sorry im just messing around - as in a 3d sphere, but also it has a fourth dimension, because unless for some reason there was no time, any 3d sphere is by default a four dimensional sphere so long as Δt>0; or something like that - so if the triangle exists for Δt>0, the triangle drawn on a 3d sphere is drawn on a 4d sphere; i guess if Δt really was zero then a Δ drawn on a sphere would only be drawn in 3 dimensions, but as far as i understand from calculus Δt can't = 0 without bad things happening to the maths - its just zeroes all the way down. i should probably get a lot less of my maths from cube 2: hypercube - ive become obsessed with visualising particles as they spiral through time; hopefully i'll get bored of this and go back to photons

anyway maths is pretty funny but it leaves itself far too open for to me doing stupid things like: E = hf & E = mc2 so for the quantum of "earth", being the smallest possible number of earths (i.e. 1 earth, because you cant have <1 earth without having 0 earths, mass = 5.972 × 10²⁴ kg), f = 356138010.4 or whatever, i probably did the actual maths part wrong, but im still laughing

mΔths
#180
toyotathon, what if i draw a triangle on a sphere with Δ sides = to 1 planck length, and then i divide it it 2 to make 3 triangles?
#181
actually i dont know whether "planck length" is really the distance i was thinking of, what im imagining is a quantum of distance
#182

toyotathon posted:

and this is cool, thanks, i understand

#183
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#184

toyotathon posted:

better explanation hopefully of the triangle internal angles on the sphere surface... when the isoceles triangle is very flat in the 5th image, area is nearly zero, and all the internal angles are around 0, 0, 180. as the point moves around the circle, along the equator, the area grows, and the two angles that were 0 grow to 180 each, when tri area is 1/2 sphere area, then when tri area is almost sphere area, the two angles which were once 0 have spun all the way around to 360. 360+360+180=900

so try this one on then:
1. Take a sphere and inflate it to a huge degree
2. draw a tiny equilateral triangle on it, to the point that the curvature of the sphere is irelevant at the level of your triangle so all 3 angles of the tiny triangle equal 60, and so the angles of the triangle = 180
3. because you are on a sphere, you have automatically drawn a 2nd triangle encompasing the rest of the sphere, where each angle is 360-60 = 300, so you've drawn two triangles on a sphere with sum of angles 900 + 180 = 1080 degrees

i think this is basically the same thing, except its all triangles

Edited by tears ()

#185
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Edited by tears ()

#186
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#187

toyotathon posted:

your question, what's the interaction between the 2D sphere and the 2D triangle in 4D:
2D is (x,y), 3D is (x,y,z), 4D we can use (x,y,z,w). so we can define a 2D sphere as (x,y,0,0) and a 2D triangle using (0,0,z,w). how many solutions are there for (x,y,0,0) = (0,0,z,w)? two 2D shapes in 4D will at best intersect at a single point. this is analogous to two 1D lines in 3D, or two 0D points in 2D. if the 2D sphere and 2D triangle are (nearly, in the limits i drew in the pic) equal then infinitely many points.

The mistake you're making is that you're defining what you call a "2d sphere" and a "2d triangle" explicitly so that the only possibility is for them to intersect at the origin. Here's a counterexample, with a "2d sphere" intersecting a "2d triangle" everywhere on the triangle:

2d sphere: all points of the form (a,b,0,0) where the distance of the point from origin is less than 2.
2d triangle: all points in the region bounded by lines between (0,0,0,0), (1,0,0,0), and (0,1,0,0)

We can agree that the shapes are right. Clearly every point in the triangle lies within the sphere.

Practically speaking, if you look at the area where these two shapes intersect in 3d, that basically describes the kinds of areas they can intersect in any larger dimension. They both sit on planes by definition. When you add a third dimension to move them around in, they don't have to be coplanar anymore and you can have them intersect in a line if you want, which you can't do without that third dimension. After 3, the other dimensions don't really add anything. The options are: they intersect nowhere, they intersect at exactly one point (when the edge of a triangle touches the edge of the circle), they intersect along a line (in 3d and above), and they intersect on a plane in whatever weird shapes you can think of.

#188
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#189
I just looked it up and apparently the volume (sphere and its contents) is called a ball, whereas what you are calling a '2d sphere' is referred to as a 2-sphere (since it is a surface with two dimensions, a type of 2-manifold). A triangle, if we include it's contents, is also a 2 manifold I believe.

I think in common language we tend to use the the words sphere and ball interchangeably.

It might be helpful to forget the analytic approach and visualize. To imagine a 2-sphere and a triangle intersecting in R4, imagine them in R3 first, but with two different colors. Color will stand in for our fourth spatial coordinate. Lets say the triangle is yellow and the sphere is red. Imagine them touching. If the intersections don't share the same color, they are not the same point in R4: yellow does not equal red, so the fourth coordinate is not identical.

Now imagine the yellow triangle remaining in place but color shifting from yellow through orange to red. Intersect the two shapes however you wish. All configurations where they intersect in this 'both red' space are true intersections in R4.

It seems clear to me that any intersections we can achieve in R3 can also be achieved in R4, if we keep the fourth coordinate, color, identical. Thus, they can intersect along at a point, a line, or not at all

#190
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#191

toyotathon posted:

thats ok, i'll watchcube 2: hupercube again, followed by its sequel cube zero

#192
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#193
every time i write the wave function symbol, ψ, it comes out as a tiny hammer and sickle
#194
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#195
That would be a good notation for replacing degrees. Degrees are essentially a remnant of Babylonian sexagesimal notation when pretty much everything else is decimal. Were stuck with them. The properties of your notation would be very helpful for trigonometry education!
#196

Belphegor posted:

That would be a good notation for replacing degrees. Degrees are essentially a remnant of Babylonian sexagesimal notation when pretty much everything else is decimal. Were stuck with them. The properties of your notation would be very helpful for trigonometry education!

We already have radians for more "theoretical" applications, but the advantages of having base 360 is that the common angles are all integer values: e.g. 15, 30, 45, 60, etc, because 360 = 2^3 * 3^2 * 5 (notice that these are descending powers of the first 3 prime numbers and 100 = 2^2*5^2 missing the power of 3), whereas if you had 1 deg be = 2pi radians, you would have to write all the common angles such as 2pi/3 = 0.3333... deg, etc. Furthermore, you wouldn't have the easy conversions that radians give you either e.g. the arclength of a circle would no longer just be theta*radius. Obviously, it's just a linear transformation, so it wouldn't be a huge deal either way, but there's little you're gaining with the conversion. Anecdotally, teaching radians to kids is harder than angles. There seems to be a bit of a conceptual hurdle to mapping the interval [0,2pi) to an angle, and I'm not sure [0,1) would improve that much. Obviously degrees are the same thing, however, it's relatively easy to show a picture of a circle split into 360 slices to illustrate how degrees work.

#197